If `(3pi)/4,sqrt(2cotalpha+1/(sin^2alpha))` is equal to `1+cotalpha` (b) `-1-cotalpha` `1-cotalpha` (d) `-1+cotalpha`

Explanation

`sqrt(2cotalpha+1/sin^2alpha)`

`=sqrt(2cotalpha+cosec^2alpha)`

`=sqrt(2cotalpha+cot^2alpha+1)`

`=sqrt((1+cotalpha)^2)`

`=|1+cotalpha|`

As `(3pi)/4 lt alpha lt pi`, `cotalpha` will be negative.

`:.|1+cotalpha| = -1-cot alpha`

So, optopon -`(b)` is the correct option.